Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 3w + 5 = 14?

Back

Subtract 5 from both sides of the equation to begin isolating w.

Front

What does it mean to 'combine like terms' in an equation?

Back

Combining like terms means to simplify an expression by adding or subtracting terms that have the same variable raised to the same power.

Front

How do you solve the equation 4x + 1 = 7x - 5?

Back

First, subtract 4x from both sides to get 1 = 3x - 5. Then, add 5 to both sides to get 6 = 3x. Finally, divide by 3 to find x = 2.

Front

What is the solution to the equation 8x + 2 + 3x + 5 = x + 12?

Back

Combine like terms to get 11x + 7 = x + 12. Then, subtract x from both sides to get 10x + 7 = 12. Subtract 7 from both sides to get 10x = 5, and divide by 10 to find x = 1/2.

Front

How do you check if your solution to a linear equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 10 = 3x - 12?

Back

Add 12 to both sides to get 22 = 3x, then divide by 3 to find x = 22/3.

Front

What is the importance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides of it are equivalent, and any operation performed on one side must also be performed on the other side to maintain equality.

Front

What is the solution to the equation 5 + 3x = 8x - 15?

Back

Subtract 3x from both sides to get 5 = 5x - 15. Then, add 15 to both sides to find 20 = 5x, and divide by 5 to get x = 4.